What is the volume of this triangular prism?

A triangular prism has length 16 feet, width 4 feet and height 9 feet.

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1 answer

To find the volume of a triangular prism, you can use the formula:

\[ \text{Volume} = \text{Base Area} \times \text{Height} \]

where the base area is the area of the triangular base and the height is the length of the prism.

  1. Determine the base area of the triangle:

The base of the triangle is the width (4 feet), and the height of the triangle (the vertical height from the base to the top vertex) is given as 9 feet. The area of a triangle is calculated with the formula:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

In this case:

  • Base = 4 feet
  • Height = 9 feet

Calculating the area:

\[ \text{Area} = \frac{1}{2} \times 4 \times 9 = \frac{1}{2} \times 36 = 18 \text{ square feet} \]

  1. Calculate the volume of the prism:

Now that we have the area of the base, we can find the volume by multiplying the base area by the length (which is 16 feet):

\[ \text{Volume} = \text{Base Area} \times \text{Length} = 18 \text{ square feet} \times 16 \text{ feet} \]

Calculating the volume:

\[ \text{Volume} = 18 \times 16 = 288 \text{ cubic feet} \]

Thus, the volume of the triangular prism is 288 cubic feet.